We can add clues and proofs of mathematical theorems to the long list of what AI is capable of: Mathematicians & AI experts have teamed up to demonstrate how machine learning can open up new avenues for us to explore in field.
Although mathematicians have used computers to discover patterns for decades, the growing power of machine learning means that these networks can process huge amounts of data & identify patterns that have never been spotted before.
In a recently published study, a research team used artificial intelligence systems developed by DeepMind, the same company that used artificial intelligence to solve complex biology problems & improve the accuracy of weather forecasts, in order to solve some long-standing math problems.
“Mathematics problems are widely regarded as some of the most difficult problems here,” said Mathematia Geordie Williamson of Sydney University in Australia.
“While mathematicians have used machine learning to help analyze complex data sets, this is the first time that we have used computers to help us formulate conjectures or suggest possible lines of attack for unproven ideas in mathematics.
The team shows that artificial intelligence is advancing proof for Kazhdan Lusztig polynomials, a mathematical problem involving the symmetry of higher dimensional algebra that has not been solved for 40 years.
The research also showed how a machine learning technique called the supervised learning model was able to identify a previously unknown relationship between two different types of mathematical knots, leading to a whole new theorem.
Knot theory in mathematics also plays a role in various other difficult areas of science, including genetics, fluid dynamics, and even the behavior of the Sun corona. The discoveries made by AI can therefore lead to breakthroughs in other areas of research.
“We have shown that, when guided by mathematical intuition, machine learning provides a powerful framework that can uncover interesting & provable conjectures in areas where a large amount of data is available or where objects are too voluminous to be studied with conventional methods. Says mathematician András Juhász of the University of Oxford in the UK.
One of the benefits of machine learning systems is the way they can search for patterns & scenarios that programmers haven’t specifically coded them to-look-out for – they take their training data & apply the same principles to new situations. .
Research shows that this type of high-speed, ultra-reliable, large-scale data processing can serve as an additional tool by working with the natural intuition of mathematicians. When it comes to complex & long equations, this can make a significant difference.
The researchers hope their work will lead to many more collaborations between academics in the fields of mathematics & artificial intelligence, opening up the possibility of discoveries that would otherwise be undiscovered.
“Artificial intelligence is an incredible tool,” says Williamson. “This work is one of the first times that it has proven its usefulness to pure mathematicians like me.
“Intuition can take us very far, but artificial intelligence can help us find connections that the human mind doesn’t always easily spot.
The research has been published in Nature.